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Lucretius in his description of the atomic theory is not generally held to demonstrate a conservation law of matter - the first and most basic conservation law of physics because it relies on the preservation of number; if you have ten stones, then no matter how you rearrange them you still have ten stones.

And this because he says that there are an infinite number of atoms (in Aristotles Physics, an infinite number of principles of first things) and one cannot add up, or sum an infinite number of things.

So one cannot have a global conservation law; still one could arguably have a local one; and this is implicit surely in his description in the following passage from the first book (on matter and void) in On the nature of things (De Rerum Natura) in the translation by AE Stallings:

... Clearly matter is not compressed

Into one heap, because we notice things becoming less,

And we perceive that, over time, everything ebbs and wanes

And old age steals them from our sight, while yet the sum remains

Undiminished.

But it is more than an assertion for he appears to provides a rationale, a justification:

This is because the particles that go

From one shrinking object cause another to grow,

Making the former shrivel up, while making the latter flower

Was this actually taken note of in the philosophical literature of Antiquity - or was it just passed over in silence; it's importance and significance not quite understood?

One might argue that the law is implicit in the Parmenidian One: from the One, only One; and it's contrapositive, from Nothing, only Nothing ('for what is not, is not').

But the Parmenidian One isn't matter in our sense; though arguably matter in its aspect of being, is an aspect of the One.

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To the extent that eternal and indestructible indivisibles (atoms) express conservation of matter we should credit it back to Leucippus and Democritus rather than Lucretius, he was simply poetizing Epicurus. However, a global conservation law does not have to be tied to counting, and by implication to a finite number. The "sum" that "remains undiminished" may just as well be interpreted as the sum (union) of atoms as elements of being, after all atomists were among the few in antiquity to admit actual infinity, to claim contra Aristotle and Euclid that magnitudes do split into indivisibles, and even to reject Euclidean geometry because it was inconsistent with existence of the smallest length. Together with postulation that each atom retains individual identity for all eternity this is a clear expression of a global conservation law. Lucretius then derives his local law from the global one: decrease of atoms in one object is exactly equal to increase in another. Or as we would say today, change of matter in any volume is equal to the flux across its boundary.

Parmenides, Plato and Aristotle meant ex nihilo nihil est in a somewhat broader sense, I believe. Not applied (just) literally, but more broadly and abstractly as a causality principle: every move needs a mover, every effect needs a cause. And of course Aristotle's causes are more than just material and effective. As for appreciation of the atomists' natural philosophic conservation law in antiquity the conditions were not right. It finds its proper context in dynamics, indeed mathematical fluid dynamics, and not only was ancient physics far removed from that, but atomists cut themselves off from even mathematical statics and kinematics by rejecting Euclidean geometry.

  • Good points; It's worth pointing out I was using 'global' in a different sense to yours; ie spatially global not temporally global; it occurs to me now, that the spatially local conservation laws imply a spatially global one - even when there is an uncountably infinite number of atoms. – Mozibur Ullah Aug 25 '15 at 5:12
  • It's also worth pointing out that the same law of flux across a boundary holds even when the shape of space is different; and this quite easily follows from the concrete imagery of Lucretious; for example, imagine drawing a circle on a table top and watching the atoms go to and for crossing the boundary; then imagine the same on a hill - there is no substantive difference as far as flux goes. – Mozibur Ullah Aug 25 '15 at 5:17
  • One could use an argument of continuity here: imagining the table top becoming hill-like; but it seems superfluous. – Mozibur Ullah Aug 25 '15 at 5:19
  • @Mozibur Ullah I added a reference on Epicurus rejecting geometry and Eudoxian astronomy, he even struck them from curriculum in his schools. The kind of geometry he envisioned was not curved but discontinuous. Epicurus postulated a minimal unit (elahiston) smaller than which something not only can not exist but even be conceived, which meant that lines do not intersect at points and there are no incommensurables. Interestingly, atoms although physically indivisible had elohiston size parts and hence shapes, that was needed to make them hook up and form objects. – Conifold Aug 25 '15 at 21:14

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